Porous plates at incidence

This paper describes the flow past two-dimensional porous plates at a Reynolds number (Re) of 30 and for a range of Darcy number (Da) and flow incidence (α) values. For a plate normal to the stream and vanishing Da, the wake shows a vortex dipole with negligible separation from the plate. With increasing Da, the separation between the vortex dipole and the plate increases; the vortex dipole shortens and is eventually annihilated at a critical Da between 8×10⁻⁴ and 9×10⁻⁴. The drag is found to decrease monotonically with Da. For any value of Da below the critical one, the vortex dipole disappears with decreasing α. However, this occurs through different topological stages for low and high Da. At low Da such as 5×10⁻⁵, as α decreases, first, one saddle-node pair merges, forming a single recirculating region with negative circulation. Thereafter, the second saddle-node pair merges, annihilating that region. For high Da, such as 5×10⁻⁴, the two saddle-node pairs merge at the same critical incidence, α=44^∘. The magnitude of lift, drag, and torque decrease with Da. However, there exists a range of Da and α, where the magnitude of the plate-wise force component increases with Da, driven by the shear on the plate's pressure side. The present findings will be directly beneficial in understanding the role of permeability and solidity on small porous and bristled wings.